officially, this is about a moving ELECTRIC charge but don't worry, it is really fun and gives the right idea.
at the upper right menu where it says "linear" change that to "circular"
and then press "go"
you will see the charge move in a circle and the waves will spread out, as if from a ciruclar antenna.

I think this Caltech thing is one of the simplest and greatest physics animations on the web.

So, by the time of the merger itself with a corresponding burst of gamma rays, the gravitational waves will have largely been emitted?

The gravitational radiation expected from a merger event (e.g. merger of two black holes) according to gtr follows a very specific qualitative sequence; the quantitative features are also distinctive. Thus the interest in LIGO/VIRGO since these will provide tests of unprecedented strength, tests of gtr in the highly nonlinear strong field regime. (Existing tests probe the weak-field regime.) This includes periodic waves with frequency increasing as the binaries near each other, with a final frequency "chirp" followed by a burst of radiation during merger itself, followed by a characteristic "ringdown", followed by exponentially decaying radiation. This scenario has been carefully explained by leading experts like Kip Thorne in various expository papers which are comprehensible (if you skip the math) by laypersons. See http://math.ucr.edu/home/baez/RelWWW/HTML/grad.html#gw for suggested reading.